Marginal false discovery rates

Estimates the marginal false discovery rate (mFDR) of a penalized regression model.

Usage

mfdr(fit, X)

Arguments

fit: An ncvreg or ncvsurv object.
X: The model matrix corresponding to fit. This is not necessary for linear regression, but in logistic and Cox regression, the mFDR depends on X. It is not necessary to supply X if it is already contained in fit; i.e., if ncvreg/ncvsurv was run with returnX=TRUE.

Value

An object with S3 class mfdr inheriting from data.frame, containing:

EF: The number of variables selected at each value of lambda, averaged over the permutation fits.
S: The actual number of selected variables for the non-permuted data.
mFDR: The estimated marginal false discovery rate (EF/S).

Details

The function estimates the marginal false discovery rate (mFDR) for a penalized regression model. The estimate tends to be accurate in most settings, but will be slightly conservative if predictors are highly correlated. For an alternative way of estimating the mFDR, typically more accurate in highly correlated cases, see perm.ncvreg().

Author

Patrick Breheny and Ryan Miller

Examples

# Linear regression --------------------------------
data(Prostate)
fit <- ncvreg(Prostate$X, Prostate$y)

obj <- mfdr(fit)
obj[1:10,]
#>                   EF S         mFDR
#> 0.84343 0.000000e+00 0 0.000000e+00
#> 0.78658 1.418692e-11 1 1.418692e-11
#> 0.73357 3.642789e-11 1 3.642789e-11
#> 0.68413 1.098086e-10 1 1.098086e-10
#> 0.63802 3.833845e-10 1 3.833845e-10
#> 0.59502 1.516932e-09 1 1.516932e-09
#> 0.55492 6.608721e-09 1 6.608721e-09
#> 0.51752 3.065378e-08 1 3.065378e-08
#> 0.48264 1.460789e-07 1 1.460789e-07
#> 0.45011 6.907848e-07 1 6.907848e-07

# Comparison with perm.ncvreg
op <- par(mfrow=c(2,2))
plot(obj)
plot(obj, type="EF")
pmfit <- perm.ncvreg(Prostate$X, Prostate$y)
plot(pmfit)
plot(pmfit, type="EF")

par(op)

# Logistic regression ------------------------------
data(Heart)
fit <- ncvreg(Heart$X, Heart$y, family="binomial")
obj <- mfdr(fit)
head(obj)
#>                   EF S         mFDR
#> 0.17746 0.000000e+00 0 0.000000e+00
#> 0.16550 6.893422e-13 1 6.893422e-13
#> 0.15435 2.683651e-11 1 2.683651e-11
#> 0.14394 6.329530e-10 1 6.329530e-10
#> 0.13424 9.776334e-09 1 9.776334e-09
#> 0.12519 1.054851e-07 1 1.054851e-07
op <- par(mfrow=c(1,2))
plot(obj)
plot(obj, type="EF")

par(op)

# Cox regression -----------------------------------
data(Lung)
fit <- ncvsurv(Lung$X, Lung$y)
obj <- mfdr(fit)
head(obj)
#>                   EF S         mFDR
#> 0.44806 0.000000e+00 0 0.000000e+00
#> 0.41786 9.926598e-06 1 9.926598e-06
#> 0.38970 3.996605e-05 1 3.996605e-05
#> 0.36344 1.392150e-04 1 1.392150e-04
#> 0.33894 4.272559e-04 1 4.272559e-04
#> 0.31610 1.173937e-03 1 1.173937e-03
op <- par(mfrow=c(1,2))
plot(obj)
plot(obj, type="EF")

par(op)